Theoretical prediction of resonance in nozzle flows

Resonance and damping in the shock movement induced either by a low-pressure ratio in a transonic convergent-divergent nozzle flow or by a supersonic or hypersonic flow in an overexpanded nozzle subject to external pressure fluctuations have been studied experimentally and numerically in the past. The underlying mechanisms for this resonance phenomenon in both cases are not fully understood. A perturbative quasi-one-dimensional model, coupled witha dual-oscillator concept, is given to explore the physical parameters that govern the shock excursion and the wave transport in the subsonic domain downstream of the shock. It is shown that the standing wave (strong resonance) in the former case is a consequence of superimposing two almost identical in amplitude but in opposite direction traveling waves through the subsonic domain inside the separated boundary layer. In the latter case, a relatively weak resonance is encountered as a result of the phasing in the convective energy transported between the energy dissipation due to the shock movement and the energy supply due to external pressure fluctuations. Resonant frequencies and pressure fluctuations compare well with the available experimental data and numerical solutions.